TCSIC,
There is a big difference between AC and DC. For AC (the 120 V AC solenoid) you cannot use a diode at all. A varistor or an RC combination is what you shall use there.
For DC, you can use diodes, but not across the contact. Put it across the coil, with cathode pointing towards the positive voltage. The diode then acts like a free-wheel for the circulating current in the coil and makes the current decay slowly instead of producing a spark between the contacts.
The slowly decaying current delays the drop-out of the coil. If that is a problem, then add a resistor in series with the diode. Select the resistor to be two or three times the coil resistance.
If that doesn't give you a fast enough release, try a varistor or a zener.
Regarding RC: For most 120 V AC coils a 0.1 or 0.22 microfarad capacitor and a 22 or 47 ohms resistor is about right for most coil sizes under 20 VA.
Diodes: Select a diode that can take the coil voltage plus a certain safety margin. I always use 1N4007, which have sufficient voltage rating for all normal coils and a 1 A current rating, which also is ample for most coils but the largest ones. As long as coil current stays below one or two amperes, a 1N4007 is OK.
Two amps? You ask. Yes, the current flows only for a short while and a diode usually can take ten times, or more, its continous rating for a few hundred milliseconds.
Google "arc suppression" for more information.